{"product_id":"intro-to-numerical-analysis-9780471467373","title":"Intro to Numerical Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn introduction to numerical analysis. This book intends to strike a balance between analytical rigor and the treatment of particular methods for engineering problems. It emphasizes on the earlier stages of numerical analysis for engineers with real life problem solving solutions applied to computing and engineering.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Zarkowski (Univ. of Alberta) offers this book as a general, advanced undergraduate work in numerical analysis, containing all of the usual topics.\" (\u003ci\u003eCHOICE\u003c\/i\u003e, October 2004)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Functional Analysis Ideas 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Some Sets 2\u003c\/p\u003e \u003cp\u003e1.3 Some Special Mappings: Metrics, Norms, and Inner Products 4\u003c\/p\u003e \u003cp\u003e1.3.1 Metrics and Metric Spaces 6\u003c\/p\u003e \u003cp\u003e1.3.2 Norms and Normed Spaces 8\u003c\/p\u003e \u003cp\u003e1.3.3 Inner Products and Inner Product Spaces 14\u003c\/p\u003e \u003cp\u003e1.4 The Discrete Fourier Series (DFS) 25\u003c\/p\u003e \u003cp\u003eAppendix 1.A Complex Arithmetic 28\u003c\/p\u003e \u003cp\u003eAppendix 1.B Elementary Logic 31\u003c\/p\u003e \u003cp\u003eReferences 32\u003c\/p\u003e \u003cp\u003eProblems 33\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Number Representations 38\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 38\u003c\/p\u003e \u003cp\u003e2.2 Fixed-Point Representations 38\u003c\/p\u003e \u003cp\u003e2.3 Floating-Point Representations 42\u003c\/p\u003e \u003cp\u003e2.4 Rounding Effects in Dot Product Computation 48\u003c\/p\u003e \u003cp\u003e2.5 Machine Epsilon 53\u003c\/p\u003e \u003cp\u003eAppendix 2.A Review of Binary Number Codes 54\u003c\/p\u003e \u003cp\u003eReferences 59\u003c\/p\u003e \u003cp\u003eProblems 59\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Sequences and Series 63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 63\u003c\/p\u003e \u003cp\u003e3.2 Cauchy Sequences and Complete Spaces 63\u003c\/p\u003e \u003cp\u003e3.3 Pointwise Convergence and Uniform Convergence 70\u003c\/p\u003e \u003cp\u003e3.4 Fourier Series 73\u003c\/p\u003e \u003cp\u003e3.5 Taylor Series 78\u003c\/p\u003e \u003cp\u003e3.6 Asymptotic Series 97\u003c\/p\u003e \u003cp\u003e3.7 More on the Dirichlet Kernel 103\u003c\/p\u003e \u003cp\u003e3.8 Final Remarks 107\u003c\/p\u003e \u003cp\u003eAppendix 3.A COordinate Rotation DIgital Computing (CORDIC) 107\u003c\/p\u003e \u003cp\u003e3.A.1 Introduction 107\u003c\/p\u003e \u003cp\u003e3.A.2 The Concept of a Discrete Basis 108\u003c\/p\u003e \u003cp\u003e3.A.3 Rotating Vectors in the Plane 112\u003c\/p\u003e \u003cp\u003e3.A.4 Computing Arctangents 114\u003c\/p\u003e \u003cp\u003e3.A.5 Final Remarks 115\u003c\/p\u003e \u003cp\u003eAppendix 3.B Mathematical Induction 116\u003c\/p\u003e \u003cp\u003eAppendix 3.C Catastrophic Cancellation 117\u003c\/p\u003e \u003cp\u003eReferences 119\u003c\/p\u003e \u003cp\u003eProblems 120\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Linear Systems of Equations 127\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 127\u003c\/p\u003e \u003cp\u003e4.2 Least-Squares Approximation and Linear Systems 127\u003c\/p\u003e \u003cp\u003e4.3 Least-Squares Approximation and Ill-Conditioned Linear Systems 132\u003c\/p\u003e \u003cp\u003e4.4 Condition Numbers 135\u003c\/p\u003e \u003cp\u003e4.5 LU Decomposition 148\u003c\/p\u003e \u003cp\u003e4.6 Least-Squares Problems and QR Decomposition 161\u003c\/p\u003e \u003cp\u003e4.7 Iterative Methods for Linear Systems 176\u003c\/p\u003e \u003cp\u003e4.8 Final Remarks 186\u003c\/p\u003e \u003cp\u003eAppendix 4.A Hilbert Matrix Inverses 186\u003c\/p\u003e \u003cp\u003eAppendix 4.B SVD and Least Squares 191\u003c\/p\u003e \u003cp\u003eReferences 193\u003c\/p\u003e \u003cp\u003eProblems 194\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Orthogonal Polynomials 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 207\u003c\/p\u003e \u003cp\u003e5.2 General Properties of Orthogonal Polynomials 207\u003c\/p\u003e \u003cp\u003e5.3 Chebyshev Polynomials 218\u003c\/p\u003e \u003cp\u003e5.4 Hermite Polynomials 225\u003c\/p\u003e \u003cp\u003e5.5 Legendre Polynomials 229\u003c\/p\u003e \u003cp\u003e5.6 An Example of Orthogonal Polynomial Least-Squares Approximation 235\u003c\/p\u003e \u003cp\u003e5.7 Uniform Approximation 238\u003c\/p\u003e \u003cp\u003eReferences 241\u003c\/p\u003e \u003cp\u003eProblems 241\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Interpolation 251\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 251\u003c\/p\u003e \u003cp\u003e6.2 Lagrange Interpolation 252\u003c\/p\u003e \u003cp\u003e6.3 Newton Interpolation 257\u003c\/p\u003e \u003cp\u003e6.4 Hermite Interpolation 266\u003c\/p\u003e \u003cp\u003e6.5 Spline Interpolation 269\u003c\/p\u003e \u003cp\u003eReferences 284\u003c\/p\u003e \u003cp\u003eProblems 285\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Nonlinear Systems of Equations 290\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 290\u003c\/p\u003e \u003cp\u003e7.2 Bisection Method 292\u003c\/p\u003e \u003cp\u003e7.3 Fixed-Point Method 296\u003c\/p\u003e \u003cp\u003e7.4 Newton–Raphson Method 305\u003c\/p\u003e \u003cp\u003e7.4.1 The Method 305\u003c\/p\u003e \u003cp\u003e7.4.2 Rate of Convergence Analysis 309\u003c\/p\u003e \u003cp\u003e7.4.3 Breakdown Phenomena 311\u003c\/p\u003e \u003cp\u003e7.5 Systems of Nonlinear Equations 312\u003c\/p\u003e \u003cp\u003e7.5.1 Fixed-Point Method 312\u003c\/p\u003e \u003cp\u003e7.5.2 Newton–Raphson Method 318\u003c\/p\u003e \u003cp\u003e7.6 Chaotic Phenomena and a Cryptography Application 323\u003c\/p\u003e \u003cp\u003eReferences 332\u003c\/p\u003e \u003cp\u003eProblems 333\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Unconstrained Optimization 341\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 341\u003c\/p\u003e \u003cp\u003e8.2 Problem Statement and Preliminaries 341\u003c\/p\u003e \u003cp\u003e8.3 Line Searches 345\u003c\/p\u003e \u003cp\u003e8.4 Newton’s Method 353\u003c\/p\u003e \u003cp\u003e8.5 Equality Constraints and Lagrange Multipliers 357\u003c\/p\u003e \u003cp\u003eAppendix 8.A MATLAB Code for Golden Section Search 362\u003c\/p\u003e \u003cp\u003eReferences 364\u003c\/p\u003e \u003cp\u003eProblems 364\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Numerical Integration and Differentiation 369\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 369\u003c\/p\u003e \u003cp\u003e9.2 Trapezoidal Rule 371\u003c\/p\u003e \u003cp\u003e9.3 Simpson’s Rule 378\u003c\/p\u003e \u003cp\u003e9.4 Gaussian Quadrature 385\u003c\/p\u003e \u003cp\u003e9.5 Romberg Integration 393\u003c\/p\u003e \u003cp\u003e9.6 Numerical Differentiation 401\u003c\/p\u003e \u003cp\u003eReferences 406\u003c\/p\u003e \u003cp\u003eProblems 406\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Numerical Solution of Ordinary Differential Equations 415\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 415\u003c\/p\u003e \u003cp\u003e10.2 First-Order ODEs 421\u003c\/p\u003e \u003cp\u003e10.3 Systems of First-Order ODEs 442\u003c\/p\u003e \u003cp\u003e10.4 Multistep Methods for ODEs 455\u003c\/p\u003e \u003cp\u003e10.4.1 Adams–Bashforth Methods 459\u003c\/p\u003e \u003cp\u003e10.4.2 Adams–Moulton Methods 461\u003c\/p\u003e \u003cp\u003e10.4.3 Comments on the Adams Families 462\u003c\/p\u003e \u003cp\u003e10.5 Variable-Step-Size (Adaptive) Methods for ODEs 464\u003c\/p\u003e \u003cp\u003e10.6 Stiff Systems 467\u003c\/p\u003e \u003cp\u003e10.7 Final Remarks 469\u003c\/p\u003e \u003cp\u003eAppendix 10.A MATLAB Code for Example 10.8 469\u003c\/p\u003e \u003cp\u003eAppendix 10.B MATLAB Code for Example 10.13 470\u003c\/p\u003e \u003cp\u003eReferences 472\u003c\/p\u003e \u003cp\u003eProblems 473\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Numerical Methods for Eigenproblems 480\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 480\u003c\/p\u003e \u003cp\u003e11.2 Review of Eigenvalues and Eigenvectors 480\u003c\/p\u003e \u003cp\u003e11.3 The Matrix Exponential 488\u003c\/p\u003e \u003cp\u003e11.4 The Power Methods 498\u003c\/p\u003e \u003cp\u003e11.5 QR Iterations 508\u003c\/p\u003e \u003cp\u003eReferences 518\u003c\/p\u003e \u003cp\u003eProblems 519\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Numerical Solution of Partial Differential Equations 525\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 525\u003c\/p\u003e \u003cp\u003e12.2 A Brief Overview of Partial Differential Equations 525\u003c\/p\u003e \u003cp\u003e12.3 Applications of Hyperbolic PDEs 528\u003c\/p\u003e \u003cp\u003e12.3.1 The Vibrating String 528\u003c\/p\u003e \u003cp\u003e12.3.2 Plane Electromagnetic Waves 534\u003c\/p\u003e \u003cp\u003e12.4 The Finite-Difference (FD) Method 545\u003c\/p\u003e \u003cp\u003e12.5 The Finite-Difference Time-Domain (FDTD) Method 550\u003c\/p\u003e \u003cp\u003eAppendix 12.A MATLAB Code for Example 12.5 557\u003c\/p\u003e \u003cp\u003eReferences 560\u003c\/p\u003e \u003cp\u003eProblems 561\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 An Introduction to MATLAB 565\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 565\u003c\/p\u003e \u003cp\u003e13.2 Startup 565\u003c\/p\u003e \u003cp\u003e13.3 Some Basic Operators, Operations, and Functions 566\u003c\/p\u003e \u003cp\u003e13.4 Working with Polynomials 571\u003c\/p\u003e \u003cp\u003e13.5 Loops 572\u003c\/p\u003e \u003cp\u003e13.6 Plotting and M-Files 573\u003c\/p\u003e \u003cp\u003eReferences 577\u003c\/p\u003e \u003cp\u003eIndex 579\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":53515427807575,"sku":"9780471467373","price":173.66,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/intro-to-numerical-analysis-9780471467373","provider":"Book Curl","version":"1.0","type":"link"}